In digital systems, the need often arises for generating sine wave voltage or sinusoidal tones. Systems employed in telephone line switching, modems, telecommunications in general and various instruments all require the synthesis of sine waves. Digital synthesis of sine waves is a well developed field. An early paper by Tierney et al, titled, "A Digital Frequency Synthesizer," appearing in IEEE Transactions of Audio Electroacoustics, Vol. AU-19, pg. 48, 1971 is an example. Later work by Wittman et al appearing in the IEEE Transactions on Acoustics Speech and Signal Processing, Vol. ASSP-27, No. 6, Dec. 1979, pg. 804-809, clearly shows a variety of digital sine wave approaches.
The general techniques that these investigators have explored has become the usual method of tone generation and is widely employed. This technique, as described in the later referenced work by Wittman, is based on the accumulation of a digital representation of phase angle increments followed by conversion of the phase to a digital signal representing the sine of the phase angle by means of a table look-up procedure. The digital value which is applied to the accumulator each sampling interval is proportional to the frequency of the sine wave generated. An analog sine wave output is derived from the digital sine values by conventional D to A conversion techniques. Any frequency of sine wave can be generated and the precision with which the tone or the wave form is generated is expressed in terms of signal to noise ratio and phase jitter at the synthesizer analog voltage output.
In a typical application such as that described in the later referenced work by Wittman et al above, the accumulator has a width of 12 bit in digital form. The read only storage table which contains the sine values has 10 bits wide addressability, each address containing a sample of 8 bits in binary length as the digital sine value for a specific 10 bit address input. Such an application clearly requires at least a 1024 by 8 bit table for the sine function values. This is a considerable portion of the overall synthesizer's complexity. Further, as greater frequency resolution is required, the number of accumulator bits must be increased because the sampling frequency cannot be made less than twice the highest known to be generated as is known from the Nyquist theory. With larger accumulator bit strings, the phase noise can be further reduced if the number of address bits in the ROS table which contains the sine values can be increased. This, of course, requires a still larger table and concommittant result of greater complexity and cost.